XSP: An IntegrationTechnology for Systems Development and Evolution Formal Specifications for Unifying XML and Relational Systems

Before the "relational revolution", developers had to understand the details of the data structures on which they operated in order to access the content. Relational theory introduced the concept of "data independence" in that the operations in the relational algebra do not need to know anything about the structure of the data in order to work. This allows analysts, designers, and programmers to do their jobs without knowledge of the structure the underlying physical data, and for database administrators to reorganize, optimize, and distribute physical databases without "breaking" applications The mathematics of the relational model is based heavily on classical set theory, CST, and this is both its strength and its weakness. For example, limitations -such as the ability to talk meaningfully only about flat tables -stem from the fact that classical set theory blurs the distinction between sets with “ordered” elements and sets with “nested” elements. Thus, operations become ill defined when extended to represent and manipulate sets with both ordered elements and nested elements. D L Childs developed an "extended set theory", XST, more than 30 years ago that adds an additional parameter known as a "scope" to the membership condition of classical set theory. In CST, membership is based on only an element component; in XST membership is based on both an element component and a scope component. This extended membership condition can be used to model ordering and containment relationships that are simply too "messy" to handle in classical set theory and the formalisms (such as relational algebra) that are based on it. XSP Technology consists of three separate formal specifications: XST: Extended Set Theory Formal axiomatic specification of extensions to the foundations of Classical set theory that support the modeling of computer based operations and operands. XSN: Extended Set Notation Formal set theoretic notation expressing operations and operands of XST that preserve the mathematical identity of all conceptual and computer-based structures being considered for a system. XSP: Extended Set Processing Formal specification of a system of XSN defined operations and operands that can be executed by a computer. In applying XSP technology to real-world problems, the "well-formedness" criterion of XML means that XML data can be formally modeled by extended set theory (XST). In other words, an XML "document" is, by its very nature, a well-defined extended set. Previous XSP research has shown the feasibility of preserving the operation-centric and data independent advantages of the relational data model (RDM) by formally modeling XML document types as extended sets (Xsets). XSP Technology also goes beyond the formal underpinnings of the relational model to describe the physical implementation of the operations and the representations of data within a computer. This has great potential to bridge the mathematically clean, but difficult world of the “pure” relational model and the messy, but more pragmatic world of XML. As the concepts of XSP technology become more widely known, they can be applied and expanded by widespread experience and experimentation. XSP technology offers the advantages of mathematical formalism to be applied to the XML world of structured documents. * Software AG supported this analysis of XSP Technology, but that company does not necessarily endorse the conclusions here, nor should any implications be drawn as to the company’s plans to support XSP Technology in its future products.